Issue 41

F. Berto et alii, Frattura ed Integrità Strutturale, 41 (2017) 79-89; DOI: 10.3221/IGF-ESIS.41.12 88 relevant to smooth and notched samples under pure tension, pure torsion and multiaxial loading conditions, regardless the nominal load ratio and the phase angle. R EFERENCES [1] Fatemi, A., Shamsaei, N., Multiaxial fatigue: An overview and some approximation models for life estimation, Int. J. Fatigue, 33 (2011) 948-958. [2] Nieslony, A., Sonsino, C.M., Comparison of some selected multiaxial fatigue assessment criteria, L.B.F. Report, No. FB-234 (2008). [3] Fatemi, A., Socie, D.F., A critical plane approach to multiaxial fatigue damage including out-of-phase loading, Fatigue Fract. Eng. Mater. Struct., 11 (1988) 149-165. [4] Fatemi, A., Kurath, P. P., Multiaxial fatigue life prediction under the influence of mean stresses, ASME J. Eng. Mater. Techn., 110 (1988) 380-388. [5] Łagoda, T., Macha, E., Bedkowski, W., A critical plane approach based on energy concepts: application to biaxial random tension-compression high-cycle fatigue regime, Int. J. Fatigue, 21 (1999) 431-443. [6] Carpinteri, A., Spagnoli, A., Multiaxial high-cycle fatigue criterion for hard metals, Int. J. Fatigue, 23 (2001) 135-145. [7] Carpinteri, A., Spagnoli, A., Vantadori, S., Bagni, C., Structural integrity assessment of metallic components under multiaxial fatigue: The C-S criterion and its evolution, Fatigue Fract. Eng. Mater., 36 (2013) 870-883. [8] Ye, D., Hertel, O., Vormwald, M., A unified expression of elastic–plastic notch stress–strain calculation in bodies subjected to multiaxial cyclic loading, Int. J. Solids Struct., 45 (2008) 6177-6189. [9] Cristofori, A., Benasciutti, D., Tovo, R., A stress invariant based spectral method to estimate fatigue life under multiaxial random loading, Int. J. Fatigue, 33 (2011) 887–899. [10] Carpinteri, A., Spagnoli, A., Vantadori, S., Reformulation in the frequency domain of a critical plane-based multiaxial fatigue criterion, Int. J. Fatigue, 67 (2014) 55-61. [11] Jasper, T.M., The value of the energy relation in the testing of ferrous metals at varying ranges and at intermediate and high temperature, Philos. Mag., 46 (1923) 609–627. [12] Ellyin, F., Cyclic strain energy density as a criterion for multiaxial fatigue failure, Brown, Miller, editors. Biaxial and Multiaxial Fatigue, London: EGF Publication, (1989) 571–83. [13] Ellyin, F., Fatigue damage, crack growth and life prediction, Edmonton: Chapman and Hall (1997). [14] Macha, E., Sonsino, C. M., Energy criteria of multiaxial fatigue failure, Fatigue Fract. Engng. Mater. Struct., 22 (1999) 1053–1070. [15] Pook, L.P., Sharples, J.K., The mode III fatigue crack growth threshold for mild steel, Int. J. Fract., 15 (1979) R223- R226. [16] Pook, L.P., The fatigue crack direction and threshold behaviour of mild steel under mixed mode I and III loading, Int. J. Fatigue, 7 (1985) 21-30. [17] Tong, J., Yates, J.R., Brown, M.W., Some aspects of fatigue thresholds under mode III and mixed mode and I loadings, Int. J. Fatigue, 18 (1986) 279-285. [18] Yu, H.C., Tanaka, K., Akiniwa, Y., Estimation of torsional fatigue strength of medium carbon steel bars with circumferential crack by the cyclic resistance-curve method, Fatigue Fract. Eng. Mater., 21 (1998) 1067-1076. [19] Tanaka, K., Akiniwa, Y., Yu, H., The propagation of a circumferential fatigue crack in medium-carbon steel bars under combined torsional and axial loadings, In: Mixed-Mode Crack Behaviour, ASTM 1359 (eds Miller, K.J., McDowell, D.L.), West Conshohocked, PA, (1999) 295-311. [20] Pippan, R., Zelger, C., Gach, E., Bichler, C., Weinhandl, H., On the mechanism of fatigue crack propagation in ductile metallic materials, Fatigue Fract. Engng. Mat. Struct., 34 (2011) 1-16. [21] Christopher, C.J., James, M.N., Patterson, E.A., Tee, K.F., Towards a new model of crack tip stress fields, Int. J. Fracture, 148 (2007) 361–371. [22] Christopher, C.J., James, M.N., Patterson, E.A., Tee, K.F., A quantitative evaluation of fatigue crack shielding forces using photoelasticity, Eng. Fract. Mech., 75 (2008) 4190-4199. [23] Berto, F., Lazzarin, P., Yates, J., Multiaxial fatigue of V-notched steel specimens: a non-conventional application of the local energy method, Fatigue Fract. Engng. Mater. Struct., 34 (2011) 921–943. [24] Lazzarin, P., Sonsino, C.M., Zambardi, R., A notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings, Fatigue Fract. Engng. Mater. Struct., 27 (2004) 127- 140.